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ECE 404 / 504
Due: Friday 15 February 2013
Transmission and Distribution Protection of Voltage Sourced Converters
Homework #3
Converter Modulation
1. Find the harmonic content of a six-step line-to- neutral voltage output waveform from a six-step
voltage sourced converter as shown in Figure 1. Use a DC line voltage of 300 Volts to determine
the voltage levels and a switching frequency of 50 Hertz (for the entire cycle, not merely the
individual steps) to determine the appropriate time intervals. In your answer, give the
magnitude of the first five non-zero voltage harmonics.
Voltage (V)
Time (sec)
Figure 1. Six step voltage sourced converter line-to-neutral output waveform
2. An induction motor has an equivalent circuit as shown in Figure 2. It is supplied from a power
converter that has a harmonic content as follows: Fundamental frequency voltage amplitude is
1.0 per unit; Fifth harmonic voltage amplitude is 0.20 per unit; Seventh harmonic voltage
amplitude is 0.143 per unit; All at zero phase angle. If you need a base for your calculations,
use 440V and 50kVA. Slip is 0.025 per unit for the 50 Hertz fundamental frequency. Use
Answers may be expressed in either per unit or SI units for full credit.
a. Find the currents and the power losses at each frequency. Remember that all reactances
and the slip are functions of the frequency at hand.
b. Why is it a bad idea to use a variable speed drive on a deep bar induction machine?
+
-
R1=0.02pu X1=j0.06pu
Vout converter
XM=j5.0pu
X2=j0.04pu
R2=0.02pu
R2 (1-slip)/slip
Figure 2. Induction motor circuit with voltage sourced converter input
There is more on the other side of this page.
ECE 404 / 504
Due: Friday 15 February 2013
Transmission and Distribution Protection of Voltage Sourced Converters
Homework #3
Converter Modulation
3. In class, we saw a MathCAD simulation of a pulse width modulated waveform using Sine
Triangle methods. For a 5.0kHz triangle wave of 1.0 peak-to-peak and an average value of zero
with a sine wave of 50 Hertz,
a. Find the voltage harmonic spectrum.
b. An interesting way to increase the available fundamental component in the output is to add
some third harmonic to the sine wave. Some loads filter out third harmonic, so this is an
easy way to get greater performance from a sine-triangle inverter. For the inverter at hand,
determine how much more fundamental frequency can be added without overmodulating.
There exists a closed form analytical solution to this problem, but it is probably easier and
more fun to let computer simulation do the work for you. Two significant figures on the
percent increase is plenty.
4. Space vectors provide a way to get specific polyphase voltages from an electronic power
converter. For a DC link voltage of 100V and a switching interval of 50µs,
a. Determine the switching time intervals appropriate to obtain an output voltage vector of 47
Volts at a phase angle of 85 degrees.
b. Find the maximum possible output voltage that can be obtained at the same 85 degrees
phase angle.
There is more on the other side of this page.